Given, and is a quadratic polynomial with leading coefficient unity. Statement I…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Given,

f(x) = \sin^3 x

and

P(x)

is a quadratic polynomial with leading coefficient unity. Statement I

\int_{0}^{2\pi} P(x) \cdot f''(x) dx

vanishes. Statement II

\int_{0}^{2\pi} f(x) dx

vanishes.